The action of an optical system can be considered as a transformation that operates on an incident wavefront to generate a transmitted wavefront. In many optical systems, different points on the wavefront experience different transformations depending on what portions of the optical system they traverse. For example, when a wave is incident on a lens, those portions of the wavefront that traverse the periphery of the lens will experience phase delays which differ from those experienced by those portions of the wavefront that illuminate the center of the lens. Since a wavefront is a locus of points having constant phase, this results in a transmitted wavefront having a shape that differs from that of the incident wavefront. By appropriately shaping and positioning lenses, one can conform the shape of the output wavefront of an optical system to a desired shape.
In some cases, an optical system is known to produce an incorrect transformation and the optical designer's role is to design a second optical system to correct that deficiency. For example, in the case of a human eye requiring a corrective lens, the optical components of the human eye perform an optical transformation that is imperfect. In another example, one might inadvertently install a flawed objective lens in a large telescope. Rather than attempting to replace the objective lens, it may be preferable to install a corrective lens. In both of these cases, it is useful for the designer of corrective lenses to know the nature of the flawed optical transformation.
An optical transformation can be pictured as the change in the shape of the wavefront illustrated in FIGS. 12A-12C, which illustrate physical principles underlying optical transformations. FIG. 12A shows a known optical system in which an incident plane wave is transformed into a spherical wave. The system in FIG. 12A is therefore representative of a human eye which does not require corrective lenses.
FIG. 12B shows a known optical system representative of a human eye in need of correction. In contrast to the system of FIG. 12A, this system shows a planar wavefront transformed into an irregular wavefront. The eye's inability to bring this irregular wavefront into focus on the retina causes the perceived image to appear distorted or blurred.
FIG. 12C shows the optical system of FIG. 12B but with an "optimal wavefront" incident on the system. The shape of this optimal wavefront is chosen such that the transformation provided by the optical system in FIG. 12B results in a spherical wavefront instead of the irregularly shaped wavefront shown in FIG. 12B. It is apparent from comparison of FIGS. 12A and 12C that a corrective optical system which transforms an incident wavefront into this optimal wavefront before the wave undergoes the flawed optical transformation has the effect of correcting for the flawed optical transformation.
Once the wavefront normal vectors at selected points on the wavefront are known, one can estimate the shape of the wavefront. Using this estimate of the wavefront shape, one can then design an optical system that corrects for the flawed optical transformation.
A common method for measuring the optical characteristics of a human eye is a simple substitution technique of placing lenses having different correction factors in front of the eye and asking the patient whether or not the overall image has improved. Using this method, a clinician can determine an overall correction for the optical characteristics of the eye. The instrument that is typically used to approximate an optical system that corrects for the flawed optical transformation of an eye is referred to as a "refractometer." In the case of a general lens system, corrections are determined by a variety of tests, each referred to by its own name, such as the "Foucault test." Throughout this specification, the term "refractometer" will be used to refer to instruments that make such tests.
The simple substitution technique determines the overall correction for the eye, but it is limited to prismatic, cylindrical, and spherical corrections. These corrections provide only the lower-order terms of the Siedel or polynomial model of the eye's optical system. The foregoing method does not correct for the errors that are specified by higher-order terms of the Siedel or polynomial model. Additionally, it is not possible, using this method, to obtain point-by-point measurements of the optimal wavefront's normal vector at designated sites on an optical system having spatial extent. For example, where the optical system is a cornea, it is not possible, using this method, to determine the optimal wavefront's normal vector at each point on the cornea.
A number of refractometers have been developed that are designed to determine the optimal wavefront at designated sites on an optical system. For example, Penney et al. U.S. Pat. No. 5,258,791, incorporated herein by this reference, describes an optical system including (i) a reference optical subsystem for projecting a reference pattern on the patient's retina through a reference area on the cornea, and (ii) a separate measurement optical subsystem for projecting a measurement pattern on the patient's retina through a measurement area on the cornea.
To determine the shape of the optimal wavefront at a designated site on the cornea using the refractometer disclosed in Penney, the measurement pattern is moved across the retina until its location coincides with the location of the reference pattern. Based on the difference between the initial and final positions of the measurement pattern, the refractometer disclosed in Penney can infer the direction of the vector normal to the optimal wavefront at the selected corneal site.
A disadvantage of the device disclosed in Penney is, simply put, that it has far too many parts. As a result, it is costly to acquire, complex to assemble, and requires frequent alignment during operation. What is therefore desirable in the art is a refractometer that provides the functionality of the Penney refractometer at reduced cost and complexity and without the need for frequent alignment.